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SUMMARY:Cascades of owls: singular integral equations in aerodynamics - Pe
 ter Baddoo ( DAMTP)
DTSTART:20181120T103000Z
DTEND:20181120T113000Z
UID:TALK114163@talks.cam.ac.uk
CONTACT:Matthew Priddin
DESCRIPTION:Porous aerofoils have excellent aeroacoustic properties\, albe
 it at the expense of aerodynamic performance. In this talk\, we will inves
 tigate the aerodynamic performance of a variety of aerofoil configurations
  through the analysis of singular integral equations. We will begin by stu
 dying the basic single rigid aerofoil problem and introduce two methods of
  solution: inversion via a Riemann-Hilbert problem and expansion in weight
 ed Chebyshev polynomials. We shall show how the former method can be exten
 ded to porous aerofoils (which satisfy a Darcy condition along their chord
 )\, but breaks down when they are undergoing unsteady motions. Consequentl
 y\, we extend the Chebyshev method to porous aerofoils by using asymptotic
  analysis to determine the parameters of a weighted Jacobi polynomial expa
 nsion. We will also apply the Riemann-Hilbert method to cascades which may
  be rigid and stationary\, porous and stationary (i.e. a cascade of owls)\
 , or rigid and moving. The latter allows many results for single aerofoils
  to be generalised to cascade geometries\, such as the Theodorsen function
  and Sears gust response function. Some preliminary experimental results i
 nto steady ground effect will also be presented.
LOCATION:CMS\, MR15
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